Finite Group DatabasebetaFinite Group DatabasebetaOrder 2432.
392 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 392 conjugacy classes of subgroups — too many to draw. Only its 121 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #11927078 | C2 | semidirect |
| 2. #11926844 | C2 | semidirect |
| 3. #11926826 | C2 | semidirect |
| 4. #11926821 | C2 | semidirect |
| 5. #11926795 | C2 | semidirect |
| 6. #11926788 | C2 | semidirect |
| 7. #11926759 | C2 | semidirect |
| 8. #11926741 | C2 | semidirect |
| 9. #11926736 | C2 | semidirect |
| 10. #11926568 | C2 | semidirect |
| 11. C19×#532 | C2 | semidirect |
| 136. #532 | D19 | semidirect |
| 184. C19 | #3251 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11927078 | 2 |
| #11926844 | 2 |
| #11926826 | 2 |
| #11926821 | 2 |
| #11926795 | 2 |
| #11926788 | 2 |
| #11926759 | 2 |
| #11926741 | 2 |
| #11926736 | 2 |
| #11926568 | 2 |
| C19×#532 | 2 |
| #3251 | 19 |